Equipollence (geometry)

Property of parallel segments that have the same length and the same direction

A definitive feature of Euclidean space is the parallelogram property of vectors: If two segments are equipollent, then they form two sides of a parallelogram:

The following passages, translated by Michael J. Crowe, show the anticipation that Bellavitis had of vector concepts:

Equipollences continue to hold when one substitutes for the lines in them, other lines which are respectively equipollent to them, however they may be situated in space. From this it can be understood how any number and any kind of lines may be summed, and that in whatever order these lines are taken, the same equipollent-sum will be obtained...
In equipollences, just as in equations, a line may be transferred from one side to the other, provided that the sign is changed...